Chapter 3 Assignment
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1 Chapter 3 Assignment AP Statistics-Adams Name: Period: Date: 1. This scatterplot shows the overall percentage of on-time arrivals versus overall mishandled baggage per 1000 passengers for the year a. Which airline has the worst record for mishandled baggage? For being on time? b. United has the highest percentage of on-time arrivals. Estimate that percentage and United s mishandled baggage rate. c. Describe the overall shape of the relationship (linearity, clusters, and influential points). d. Is there a positive or negative relationship between the on-time percentage and the rate of mishandled baggage? What is the strength of the relationship?
2 2. The best estimate of the correlation coefficient for the following scatterplot is A. 0 B. 0.1 C. 0.5 D. 0.8 E Which of these scatterplots has a least squares regression line with slope closest to zero? A. B. C. D. E.
3 4. Using data from a sample of 15 women, this scatterplot shows the relationship between body density (as compared to water density) and skinfold thickness (in mm). Skinfold thickness is used to predict body density. Choose the correct regression equation and correlation for these data. A. density = skinfold; r = B. density = skinfold; r = 0.90 C. density = skinfold; r = 0.90 D. density = skinfold; r = E. none of the above 5. Data on the diameter (in inches) and the age (in years) of a sample of 25 oak trees yielded the regression equation diameter = age and the residual plot shown here. a. Which of these is the best explanation of the relationship between growth in diameter and age of tree? A. The diameter grows at approximately inch per year throughout the life of the tree. B. The diameter grows slower than inch per year early in the life of the tree and faster than inch per year later in life. C. The diameter grows faster than inch per year early in the life of the tree and slower than inch per year later in life. D. The diameter grows at a rate of 1.18 inches per year throughout the life of the tree. b. If the standard deviation of the diameters is 2.2 inches and the standard deviation of the ages is 12 years, find the correlation between diameter and age. c. Is the correlation coefficient a good measure of association to use with the diameter versus age data? Briefly explain your answer.
4 6. A friend is planning to sell her used Honda so she gathers data on prices (in thousands of dollars) and year (let 79 represent 1979) for eleven cars similar to hers. A scatterplot of the data is shown. The least squares regression line through these data has the equation price = year a. Interpret the slope of the regression line in the context of this problem. b. The data point for the 1979 Honda is removed from the data set, and a new regression model is calculated. State whether the slope increases or decreases. c. Your friend s Honda is a Use the regression model to establish a selling price for her car. d. Looking at these data, do you think the selling price established in part c is too high, too low, or about right? Explain.
5 7. Here is the regression analysis for calories versus fat (in grams) for some pizza data. a. Compute 2 R (R-sq). b. Interpret 2 R in the context of this problem. 8. How much do consumers in the United States pay for gas? These data show typical prices (in thousands of dollars) and highway gas mileages for a sample of car models commonly sold in the United States. The scatterplot of these data with a regression line is also displayed on the next page, followed by a residual plot. Model Price (thousands $) MPG Chevrolet Suburban LS Dodge Caravan EX Ford Explorer XLS Ford Focus SE Ford Taurus Honda Civic EX Hyundai Elantra GL Lexus GS Saturn L Toyota Corolla CE Volvo S
6 a. Interpret the slope of the regression line in the context of this problem. b. Is fitting a regression line appropriate for the pattern displayed in the scatterplot? Explain by inspecting the original plot as well as the residual plot. c. What lurking variable might account for the negative association between price and gas mileage? d. Which auto produces the largest positive residual? Compute that residual. (Do not round your answer.)
7 9. For a laboratory experiment, scientists induced a skin infection in a rat and recorded the growth of the discolored skin patch every three days over a six-week period. Ten of the recordings are shown here. Days After Induction Diameter of Patch (mm) a. Plot diameter versus days on your calulator and sketch the graph shown on your screen below. b. Gillian thought that the growth in the diameter should be exponential. What transformation should Gillian use on these data before she fits a linear equation? c. Make this transformation, and find the equation of the regression line for the transformed data. d. Show a sketch of the residuals from your calculator, and comment on the observed pattern. e. Use your model from part c to estimate the rate of growth of the patch. From examining the residuals, does it appear that this rate will be constant?
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